Biomedical subjects

Epifanio G Virga

Publications and source records attributed to Epifanio G Virga.

13 recordsLinked to original sources

PubMed2006

Quadrupolar projection of excluded-volume interactions in biaxial nematic liquid crystals.

We compute the quadrupolar approximation to the excluded-volume interaction between hard spherocuboids, which applies to both platelets and spheroplatelets as special cases. We show that this approximation can be written as the superposition of two London interactions: one attractive and the other repulsive. This conclusion also proves why the phase diagram for the excluded-volume interaction of spherocuboids is expected to feature a direct isotropic-to-biaxial transition at a single Landau point.

Journal Article↗

PubMed2006

Universal mean-field phase diagram for biaxial nematics obtained from a minimax principle.

We study a class of quadratic Hamiltonians which describe both fully attractive and partly repulsive molecular interactions, characteristic of biaxial liquid crystal molecules. To treat the partly repulsive interactions we establish a minimax principle for the associated mean-field free energy. We show that the phase diagram described by Sonnet [Phys. Rev. E 67, 061701 (2003)] is universal. Our predictions are in good agreement with the recent observations on both V-shaped and tetrapodal molecules.

Journal Article↗

PubMed2006

Residual stability of sessile droplets with negative line tension.

We study the local stability of a sessile droplet with nonvanishing line tension along the contact line, where three phases are in equilibrium. We confirm Widom's results [J. Phys. Chem. 99, 2803 (1995)] on the local stability of a droplet with positive line tension in a larger class of perturbations. When the line tension is negative, we prove that the restricted class of perturbations employed by Widom fails to capture the instability of equilibria. A notion of residual stability is introduced, which makes quantitative the condition under which equilibrium of droplets with negative line tension are likely to be observed.

Journal Article↗

PubMed2005

Bifurcation analysis and computer simulation of biaxial liquid crystals.

We extend the analysis of a mean-field model for biaxial liquid crystals recently proposed by Sonnet et al. [Phys. Rev. E 67, 061701 (2003)]. In particular, we perform a bifurcation analysis of the equilibrium equations and derive the complete phase diagram. We show that two order parameters suffice to label all equilibrium phases, though they exhibit different bifurcation patterns. A Monte Carlo simulation study is performed as well, confirming qualitatively the predictions of this analysis.

Comment↗

PubMed2005

Tricritical points in biaxial liquid crystal phases.

We further pursue the analysis of a mean-field model recently proposed by Sonnet [Phys. Rev. E 67, 061701 (2003)] to describe nematic biaxial phases. This model, which is based on a simplified version of Straley's pair potential, is characterized by the prediction of a tricritical point along the transition line between uniaxial and biaxial phases. We show that the same model predicts another tricritical point, but along the line of the direct isotropic-to-biaxial transition. Our prediction is quantitative, as it stems from an analytical criterion for tricriticality.

Journal Article↗

PubMed2005

Mechanical actions on nanocylinders in nematic liquid crystals.

We apply the Landau-de Gennes theory to study the equilibrium problem that arises when a cylinder of radius R is kept at a given distance h from a plane wall. We assume that both the lateral boundary of the cylinder and the wall enforce homeotropic anchoring conditions on the liquid crystal, which prescribe the liquid crystal molecules to stick orthogonally to the bounding surfaces. Typically, in our study R ranges from a few to hundreds of biaxial coherence lengths, where a biaxial coherence length, which depends on the temperature, is a few nanometers. The equilibrium textures exhibit a bifurcation between a flat solution, where one eigenvector of the order tensor Q is everywhere parallel to the cylinder's axis, and an escape solution, where the eigenframe of Q flips out of the plane orthogonal to the cylinder's axis. The escape texture minimizes an appropriately renormalized energy functional F(*) for h>h(c), while the flat texture minimizes F(*) for h< h(c). We compute both the force and the torque transmitted to the cylinder by the surrounding liquid crystal and we find that the diagrams of both as functions of h fail to be monotonic along the escape texture. Thus, upon decreasing h, a snapping instability is predicted to occur, with an associated hysteresis loop in the force diagram, before h reaches h(c). Finally, since the symmetry of this problem makes it equivalent to the one where two parallel cylinders are separated by the distance 2h , the snapping instability predicted here should also be observed there.

Journal Article↗

PubMed2004

Nanomechanics of order reconstruction in nematic liquid crystals.

We employ a continuum model to compute both torque and force transmitted through a thin twist cell filled with a nematic liquid crystal and bounded by flat plates with anchorings at right angles. The transmitted torque vanishes at the order reconstruction threshold when the cell thickness is comparable with the biaxial coherence length. At the same point, the force diagram exhibits an angular point which disappears above a critical twist mismatch. Both torque and force diagrams against the cell's thickness fail to be monotonic when the total twist is near pi/2 .

Journal Article↗

PubMed2004

Sign of line tension in liquid bridge stability.

We apply the stability criterion we recently proposed for a general wetting functional [Phys. Rev. E 68, 012601 (2003)] to find out whether straight liquid bridges can be stable when subject to line tension of either sign. Our main conclusion is that, even when the line tension is negative, a straight liquid bridge can be stable, and so observable, provided that the line tension is not too large in absolute value.

Journal Article↗

PubMed2004

Local elastic stability for nematic liquid crystals.

We derive a stability criterion for nematic liquid crystals from a general study of the second variation of Frank's elastic free-energy functional. When applied to elementary director alignments compatible with the boundary conditions, such as the uniform alignment in a hybrid cell, this criterion is able to determine whether the most likely destabilizing mode is periodic or not, and to estimate the modulation length of such a mode, when it is periodic.

Journal Article↗

PubMed2003

Order reconstruction in frustrated nematic twist cells.

Within the Landau-de Gennes theory of liquid crystals, we study the equilibrium configurations of a nematic cell with twist boundary conditions. Under the assumption that the order tensor Q be uniaxial on both bounding plates, we find three separate classes of solutions, one of which contains the absolute energy minimizer, a twistlike solution that exists for all values of the distance d between the plates. The solutions in the remaining two classes exist only if d exceeds a critical value d(c). One class consists of metastable, twistlike solutions, while the other consists of unstable, exchangelike solutions, where the eigenvalues of Q are exchanged across the cell. When d=d(c), the metastable solution relaxes back to the absolute energy minimizer, undergoing an order reconstruction somewhere within the cell. The critical distance d(c) equals, in general, a few biaxial coherence lengths. This scenario applies to all the values of the boundary twist but pi/2, which thus appears as a very special case, though it is the one more studied in the literature. In fact, when the directors prescribed on the two plates are at right angles, two symmetric twistlike solutions merge continuously into an exchangelike solution at the critical value of d where the latter becomes unstable. Our analysis shows how the classical bifurcation associated with this phenomenon is unfolded by perturbing the boundary conditions.

Journal Article↗

PubMed2003

General stability criterion for wetting.

We propose a general stability criterion for the wetting of solid substrates, both arbitrarily curved and inhomogeneous. In addition to the classical surface tension, the adhering drops can also exhibit a tension along the contact line where three phases meet, namely, the solid, the liquid, and the environment fluid. Moreover, we show how some stability issues currently debated in the specialized literature of disparate fields could profit from the application of this general criterion.

Journal Article↗

PubMed2003

Dielectric shape dispersion and biaxial transitions in nematic liquid crystals.

Using two order tensors, we propose a mean-field model to describe the uniaxial and biaxial phases of nematogenic molecules presenting a shape dispersion of their biaxial dielectric susceptibility. We recover the classical isotropic-uniaxial-biaxial sequence of phases. The phase diagram exhibits a tricritical point, a feature that cannot be retraced in the other mean-field models established for molecules without shape dispersion.

Journal Article↗

PubMed2002

Core hysteresis in nematic defects.

We study field-induced transformations in the biaxial core of a nematic disclination with strength m=1, employing the Landau-de Gennes order tensor parameter Q. We first consider the transition from the defectless escaped radial structure into the structure hosting a line defect with a negative uniaxial order parameter along the axis of a cylinder of radius R. The critical field of the transition monotonically increases with R and asymptotically approaches a value corresponding to xi(b)/xi(f) approximately 0.3, where the correlation lengths xi(b) and xi(f) are related to the biaxial order and the external field, respectively. Then, in the same geometry, we focus on the line defect structure with a positive uniaxial ordering along the axis, surrounded by the uniaxial sheath, the uniaxial cylinder of radius xi(u) with negative order parameter and director in the transverse direction. We study the hysteresis in the position of the uniaxial sheath upon increasing and decreasing the field strength. In general, two qualitatively different solutions exist, corresponding to the uniaxial sheath located close to the defect symmetry axis or close to the cylinder wall. This latter solution exists only for strong enough anchorings. The uniaxial sheath is for a line defect what the uniaxial ring is for a point defect: by resorting to an approximate analytic estimate, we show that essentially the same hysteresis exhibited by the uniaxial sheath is expected to occur at the uniaxial ring in the core structure of a point defect.

Journal Article↗